National parks in at least four states could soon reopen to visitors during the government shutdown.

Concerned about the shutdown's impact on the tourism industry, the governors of Utah, South Dakota, Arizona and Colorado have asked the Obama administration to allow them to foot the bill to return their states' parks to normal operations.

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Interior Secretary Sally Jewell today responded positively to the request, pledging to "consider agreements" with the governors to help circumvent a lapse in federal appropriations. She also personally called several governors to discuss the issue, ABC News has learned.

"The Interior Department will begin conversations about how to proceed as expeditiously as current limited resources allow," Interior Department spokesman Blake Androff said in a statement to ABC News.

"We continue to call on Congress to act swiftly to enact appropriations for the entire government so that we can re-open all 401 national parks for the American people," he said.

The department gave no estimate for when exactly the parks might return to business. Administration officials say the parks would remain under federal government control but be funded through by the state.

All 401 national parks have been shut to visitors since Oct. 1, and more than 20,000 National Park Service employees have been furloughed without pay from their jobs. The closures have also hurt many local communities and businesses that rely on tourism to survive.

"This is major news for the Grand Canyon National Park and the many other national parks and monuments in my district and across Arizona," Rep. Ann Kirkpatrick, D-Ariz., said. "These destinations bring millions of dollars into our local economy, which has taken a tremendous direct hit during the shutdown."

The Coalition of National Park Service Retirees estimates that more than 7 million visitors have been turned away from all 401 parks during the government shutdown so far, costing $76 million a day in lost revenue for the parks and local economies.

ABC News' John Parkinson and Arlette Saenz contributed to this report.